Riemann–Liouville fractional stochastic evolution equations driven by both Wiener process and fractional Brownian motion

Yang, Min; Gu, Hong

doi:10.1186/s13660-020-02541-3

Cited by 4 publications

(3 citation statements)

References 24 publications

(20 reference statements)

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“…Refs. [12,13] established the existence of mild solutions for a class of stochastic evolution equations with Riemann-Liouville fractional derivatives. Additionally, refs.…”

Section: Introductionmentioning

confidence: 99%

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Zhou

2023

Fractal Fract

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In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order μ∈(1,2) and type ν∈[0,1]. We prove the existence of mild solutions of Hilfer fractional stochastic evolution equations when the semigroup is compact as well as noncompact. Our approach is based on the Schauder fixed point theorem, the Ascoli–Arzelà theorem and the Kuratowski measure of noncompactness. An example is also provided, to demonstrate the efficacy of this method.

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“…Refs. [12,13] established the existence of mild solutions for a class of stochastic evolution equations with Riemann-Liouville fractional derivatives. Additionally, refs.…”

Section: Introductionmentioning

confidence: 99%

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Zhou

2023

Fractal Fract

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“…where the constant C comes from Step 1. Inserting Equation (17) in Equation ( 11), the required result is obtained with constants:…”

Section: Existence and Uniquenessmentioning

confidence: 99%

“…A considerable amount of literature has been published on the existence and uniqueness of solutions for FSDEs. One can see [9][10][11][12][13][14][15][16][17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

et al. 2021

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In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results.

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On the existence and uniqueness of the solution to multifractional stochastic delay differential equation

Bouguetof,

Mezdoud,

Kebiri

et al. 2024

Fract Calc Appl Anal

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In this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results.

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Riemann–Liouville fractional stochastic evolution equations driven by both Wiener process and fractional Brownian motion

Cited by 4 publications

References 24 publications

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order μ∈(1,2)

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

On the existence and uniqueness of the solution to multifractional stochastic delay differential equation

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